A central task in vision is to represent objects as the same persisting individuals even through visual interruptions such as occlusion. Previous research in several areas of cognitive science has identified a powerful principle in such processing: objects must trace continuous paths through space and time. Here, we report novel fMRI evidence for the neural consequences of spatiotemporally continuous vs. discontinuous motion. We measured fMRI adaptation to reveal whether the fusiform face area treats two faces as the same or different (Grill-Spector et al., 1999; Kourtzi & Kanwisher, 2001). The initial display on each trial contained two vertical columns spanning fixation. One face appeared from behind a column, moved to fixation, turned back, and disappeared behind the original column. Immediately afterwards, a second (same or different) face made a similar movement from either the same column (which would be consistent with its being the same reappearing object) or the other column (which would necessarily be a new object, even if it was featurally identical). We hypothesized that two identical faces from the same column would be treated as the same persisting object, resulting in fMRI adaptation. In contrast, we predicted that two identical faces from different columns would be treated as separate objects, reducing fMRI adaptation. Significant fMRI adaptation occurred only when two identical faces were linked as a single object via spatiotemporal continuity. These results provide a novel demonstration of how spatiotemporal cues to object persistence can influence neural processing of object identity in mid-level visual cortical areas.